i'm guessing it's a gas dryer. in the back of the dryer, there is a hose that plugs into a hole in the wall, leading to the outside. this is for the exhaust of the warm air that goes into the dryer. pull your dryer out and see the pipe in the wall where the exhaust hose plugs into is clogged.
we once had a dryer which we thought was broken because there was no longer any heat, but we found that the hole (exhaust) in the wall was just super clogged with lint from use over the years. we washed it out with a garden hose, and it worked again.
maybe the kenmore keeps shutting off because it can't get rid of the used air. hope this helps.
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